LMFDB - Embedded newform 360.2.q.e.241.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(121,360)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("360.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.3
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	360.241
Dual form			360.2.q.e.121.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05903 + 1.37057i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.51859 + 2.63027i) q^{7} +(-0.756906 + 2.90295i) q^{9} +O(q^{10})$	\(q+(1.05903 + 1.37057i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.51859 + 2.63027i) q^{7} +(-0.756906 + 2.90295i) q^{9} +(-2.63557 + 4.56494i) q^{11} +(0.256906 + 0.444974i) q^{13} +(0.657430 - 1.60243i) q^{15} +2.80320 q^{17} +8.29877 q^{19} +(-5.21319 + 0.704213i) q^{21} +(-2.51859 - 4.36232i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.78027 + 2.03692i) q^{27} +(2.39248 - 4.14389i) q^{29} +(4.29408 + 7.43756i) q^{31} +(-9.04771 + 1.22219i) q^{33} +3.03717 q^{35} -6.58816 q^{37} +(-0.337795 + 0.823348i) q^{39} +(-3.99088 - 6.91240i) q^{41} +(0.598399 - 1.03646i) q^{43} +(2.89248 - 0.795973i) q^{45} +(4.81267 - 8.33578i) q^{47} +(-1.11221 - 1.92640i) q^{49} +(2.96868 + 3.84198i) q^{51} -0.467941 q^{53} +5.27114 q^{55} +(8.78865 + 11.3740i) q^{57} +(0.378666 + 0.655869i) q^{59} +(0.135572 - 0.234817i) q^{61} +(-6.48610 - 6.39924i) q^{63} +(0.256906 - 0.444974i) q^{65} +(3.63080 + 6.28872i) q^{67} +(3.31159 - 8.07172i) q^{69} +1.48619 q^{71} +5.31701 q^{73} +(-1.71646 + 0.231865i) q^{75} +(-8.00469 - 13.8645i) q^{77} +(7.98175 - 13.8248i) q^{79} +(-7.85419 - 4.39451i) q^{81} +(-6.03240 + 10.4484i) q^{83} +(-1.40160 - 2.42764i) q^{85} +(8.21319 - 1.10946i) q^{87} +15.2529 q^{89} -1.56053 q^{91} +(-5.64611 + 13.7619i) q^{93} +(-4.14938 - 7.18694i) q^{95} +(3.18187 - 5.51116i) q^{97} +(-11.2569 - 11.1062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + q^7	$ 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.05903	+	1.37057i	0.611432	+	0.791297i
$3$	1.05903	+	1.37057i	0.611432	+	0.791297i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.51859	+	2.63027i	−0.573972	+	0.994148i	0.422181	+	0.906512i	$0.361265\pi$
$7$	−1.51859	+	2.63027i	−0.573972	+	0.994148i	−0.996153	+	0.0876366i	$0.972069\pi$
$8$		0			0
$9$	−0.756906	+	2.90295i	−0.252302	+	0.967649i
$10$		0			0
$11$	−2.63557	+	4.56494i	−0.794655	+	1.37638i	0.128403	+	0.991722i	$0.459015\pi$
$11$	−2.63557	+	4.56494i	−0.794655	+	1.37638i	−0.923058	+	0.384660i	$0.874319\pi$
$12$		0			0
$13$	0.256906	+	0.444974i	0.0712528	+	0.123414i	0.899451	−	0.437022i	$-0.143967\pi$
$13$	0.256906	+	0.444974i	0.0712528	+	0.123414i	−0.828198	+	0.560436i	$0.810634\pi$
$14$		0			0
$15$	0.657430	−	1.60243i	0.169748	−	0.413746i
$16$		0			0
$17$	2.80320			0.679876			0.339938	−	0.940448i	$-0.389594\pi$
$17$	2.80320			0.679876			0.339938	+	0.940448i	$0.389594\pi$
$18$		0			0
$19$	8.29877			1.90387			0.951934	−	0.306304i	$-0.0990923\pi$
$19$	8.29877			1.90387			0.951934	+	0.306304i	$0.0990923\pi$
$20$		0			0
$21$	−5.21319	+	0.704213i	−1.13761	+	0.153672i
$22$		0			0
$23$	−2.51859	−	4.36232i	−0.525162	−	0.909607i	−0.999571	−	0.0293020i	$-0.990672\pi$
$23$	−2.51859	−	4.36232i	−0.525162	−	0.909607i	0.474409	−	0.880305i	$-0.342662\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.78027	+	2.03692i	−0.919963	+	0.392005i
$28$		0			0
$29$	2.39248	−	4.14389i	0.444272	−	0.769502i	−0.553729	−	0.832697i	$-0.686796\pi$
$29$	2.39248	−	4.14389i	0.444272	−	0.769502i	0.998001	+	0.0631952i	$0.0201291\pi$
$30$		0			0
$31$	4.29408	+	7.43756i	0.771239	+	1.33583i	0.936884	+	0.349640i	$0.113696\pi$
$31$	4.29408	+	7.43756i	0.771239	+	1.33583i	−0.165645	+	0.986185i	$0.552970\pi$
$32$		0			0
$33$	−9.04771	+	1.22219i	−1.57500	+	0.212756i
$34$		0			0
$35$	3.03717			0.513376
$36$		0			0
$37$	−6.58816			−1.08309			−0.541543	−	0.840673i	$-0.682160\pi$
$37$	−6.58816			−1.08309			−0.541543	+	0.840673i	$0.682160\pi$
$38$		0			0
$39$	−0.337795	+	0.823348i	−0.0540905	+	0.131841i
$40$		0			0
$41$	−3.99088	−	6.91240i	−0.623270	−	1.07954i	−0.988873	−	0.148765i	$-0.952470\pi$
$41$	−3.99088	−	6.91240i	−0.623270	−	1.07954i	0.365602	−	0.930771i	$-0.380863\pi$
$42$		0			0
$43$	0.598399	−	1.03646i	0.0912549	−	0.158058i	−0.816784	−	0.576943i	$-0.804246\pi$
$43$	0.598399	−	1.03646i	0.0912549	−	0.158058i	0.908039	+	0.418885i	$0.137579\pi$
$44$		0			0
$45$	2.89248	−	0.795973i	0.431185	−	0.118657i
$46$		0			0
$47$	4.81267	−	8.33578i	0.701999	−	1.21590i	−0.265764	−	0.964038i	$-0.585624\pi$
$47$	4.81267	−	8.33578i	0.701999	−	1.21590i	0.967764	−	0.251861i	$-0.0810424\pi$
$48$		0			0
$49$	−1.11221	−	1.92640i	−0.158887	−	0.275201i
$50$		0			0
$51$	2.96868	+	3.84198i	0.415698	+	0.537984i
$52$		0			0
$53$	−0.467941			−0.0642766			−0.0321383	−	0.999483i	$-0.510232\pi$
$53$	−0.467941			−0.0642766			−0.0321383	+	0.999483i	$0.510232\pi$
$54$		0			0
$55$	5.27114			0.710761
$56$		0			0
$57$	8.78865	+	11.3740i	1.16409	+	1.50652i
$58$		0			0
$59$	0.378666	+	0.655869i	0.0492981	+	0.0853868i	0.889621	−	0.456699i	$-0.150968\pi$
$59$	0.378666	+	0.655869i	0.0492981	+	0.0853868i	−0.840323	+	0.542085i	$0.817635\pi$
$60$		0			0
$61$	0.135572	−	0.234817i	0.0173582	−	0.0300653i	−0.857216	−	0.514957i	$-0.827808\pi$
$61$	0.135572	−	0.234817i	0.0173582	−	0.0300653i	0.874574	+	0.484892i	$0.161141\pi$
$62$		0			0
$63$	−6.48610	−	6.39924i	−0.817172	−	0.806228i
$64$		0			0
$65$	0.256906	−	0.444974i	0.0318652	−	0.0551922i
$66$		0			0
$67$	3.63080	+	6.28872i	0.443572	+	0.768290i	0.997952	−	0.0639743i	$-0.0203776\pi$
$67$	3.63080	+	6.28872i	0.443572	+	0.768290i	−0.554379	+	0.832264i	$0.687044\pi$
$68$		0			0
$69$	3.31159	−	8.07172i	0.398668	−	0.971721i
$70$		0			0
$71$	1.48619			0.176378			0.0881891	−	0.996104i	$-0.471892\pi$
$71$	1.48619			0.176378			0.0881891	+	0.996104i	$0.471892\pi$
$72$		0			0
$73$	5.31701			0.622309			0.311155	−	0.950359i	$-0.399284\pi$
$73$	5.31701			0.622309			0.311155	+	0.950359i	$0.399284\pi$
$74$		0			0
$75$	−1.71646	+	0.231865i	−0.198200	+	0.0267734i
$76$		0			0
$77$	−8.00469	−	13.8645i	−0.912219	−	1.58001i
$78$		0			0
$79$	7.98175	−	13.8248i	0.898017	−	1.55541i	0.0679921	−	0.997686i	$-0.478341\pi$
$79$	7.98175	−	13.8248i	0.898017	−	1.55541i	0.830025	−	0.557726i	$-0.188326\pi$
$80$		0			0
$81$	−7.85419	−	4.39451i	−0.872687	−	0.488279i
$82$		0			0
$83$	−6.03240	+	10.4484i	−0.662142	+	1.14686i	0.317910	+	0.948121i	$0.397019\pi$
$83$	−6.03240	+	10.4484i	−0.662142	+	1.14686i	−0.980052	+	0.198742i	$0.936314\pi$
$84$		0			0
$85$	−1.40160	−	2.42764i	−0.152025	−	0.263315i
$86$		0			0
$87$	8.21319	−	1.10946i	0.880546	−	0.118947i
$88$		0			0
$89$	15.2529			1.61680			0.808402	−	0.588631i	$-0.200333\pi$
$89$	15.2529			1.61680			0.808402	+	0.588631i	$0.200333\pi$
$90$		0			0
$91$	−1.56053			−0.163588
$92$		0			0
$93$	−5.64611	+	13.7619i	−0.585475	+	1.42705i
$94$		0			0
$95$	−4.14938	−	7.18694i	−0.425718	−	0.737365i
$96$		0			0
$97$	3.18187	−	5.51116i	0.323070	−	0.559573i	−0.658050	−	0.752974i	$-0.728618\pi$
$97$	3.18187	−	5.51116i	0.323070	−	0.559573i	0.981120	+	0.193401i	$0.0619518\pi$
$98$		0			0
$99$	−11.2569	−	11.1062i	−1.13136	−	1.11621i
$100$		0			0
$101$	1.03717	−	1.79644i	0.103203	−	0.178752i	−0.809800	−	0.586706i	$-0.800424\pi$
$101$	1.03717	−	1.79644i	0.103203	−	0.178752i	0.913002	+	0.407954i	$0.133758\pi$
$102$		0			0
$103$	−2.52805	−	4.37871i	−0.249096	−	0.431447i	0.714179	−	0.699963i	$-0.246800\pi$
$103$	−2.52805	−	4.37871i	−0.249096	−	0.431447i	−0.963275	+	0.268516i	$0.913467\pi$
$104$		0			0
$105$	3.21646	+	4.16265i	0.313894	+	0.406233i
$106$		0			0
$107$	−13.2901			−1.28480			−0.642400	−	0.766370i	$-0.722061\pi$
$107$	−13.2901			−1.28480			−0.642400	+	0.766370i	$0.722061\pi$
$108$		0			0
$109$	8.34549			0.799353			0.399676	−	0.916656i	$-0.369122\pi$
$109$	8.34549			0.799353			0.399676	+	0.916656i	$0.369122\pi$
$110$		0			0
$111$	−6.97706	−	9.02951i	−0.662234	−	0.857043i
$112$		0			0
$113$	2.55098	+	4.41844i	0.239976	+	0.415651i	0.960707	−	0.277564i	$-0.0895269\pi$
$113$	2.55098	+	4.41844i	0.239976	+	0.415651i	−0.720731	+	0.693215i	$0.756194\pi$
$114$		0			0
$115$	−2.51859	+	4.36232i	−0.234859	+	0.406788i
$116$		0			0
$117$	−1.48619	+	0.408980i	−0.137398	+	0.0378102i
$118$		0			0
$119$	−4.25691	+	7.37318i	−0.390230	+	0.675898i
$120$		0			0
$121$	−8.39248	−	14.5362i	−0.762953	−	1.32147i
$122$		0			0
$123$	5.24744	−	12.7902i	0.473146	−	1.15325i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.0830			−0.983461			−0.491731	−	0.870747i	$-0.663635\pi$
$127$	−11.0830			−0.983461			−0.491731	+	0.870747i	$0.663635\pi$
$128$		0			0
$129$	2.05426	−	0.277495i	0.180867	−	0.0244321i
$130$		0			0
$131$	−0.775579	−	1.34334i	−0.0677627	−	0.117368i	0.830153	−	0.557535i	$-0.188253\pi$
$131$	−0.775579	−	1.34334i	−0.0677627	−	0.117368i	−0.897916	+	0.440167i	$0.854919\pi$
$132$		0			0
$133$	−12.6024	+	21.8280i	−1.09277	+	1.89273i
$134$		0			0
$135$	4.15416	+	3.12137i	0.357533	+	0.268645i
$136$		0			0
$137$	2.40629	−	4.16782i	0.205583	−	0.356080i	−0.744735	−	0.667360i	$-0.767424\pi$
$137$	2.40629	−	4.16782i	0.205583	−	0.356080i	0.950318	+	0.311280i	$0.100758\pi$
$138$		0			0
$139$	10.7329	+	18.5898i	0.910349	+	1.57677i	0.813572	+	0.581464i	$0.197520\pi$
$139$	10.7329	+	18.5898i	0.910349	+	1.57677i	0.0967767	+	0.995306i	$0.469147\pi$
$140$		0			0
$141$	16.5215	−	2.23177i	1.39136	−	0.187949i
$142$		0			0
$143$	−2.70837			−0.226486
$144$		0			0
$145$	−4.78496			−0.397369
$146$		0			0
$147$	1.46240	−	3.56448i	0.120617	−	0.293993i
$148$		0			0
$149$	7.39717	+	12.8123i	0.605999	+	1.04962i	0.991893	+	0.127078i	$0.0405600\pi$
$149$	7.39717	+	12.8123i	0.605999	+	1.04962i	−0.385893	+	0.922543i	$0.626107\pi$
$150$		0			0
$151$	−0.490876	+	0.850223i	−0.0399469	+	0.0691901i	−0.885308	−	0.465006i	$-0.846052\pi$
$151$	−0.490876	+	0.850223i	−0.0399469	+	0.0691901i	0.845361	+	0.534196i	$0.179386\pi$
$152$		0			0
$153$	−2.12176	+	8.13754i	−0.171534	+	0.657882i
$154$		0			0
$155$	4.29408	−	7.43756i	0.344909	−	0.597399i
$156$		0			0
$157$	3.43077	+	5.94226i	0.273805	+	0.474244i	0.969833	−	0.243770i	$-0.0783843\pi$
$157$	3.43077	+	5.94226i	0.273805	+	0.474244i	−0.696028	+	0.718015i	$0.745051\pi$
$158$		0			0
$159$	−0.495564	−	0.641344i	−0.0393008	−	0.0508619i
$160$		0			0
$161$	15.2988			1.20571
$162$		0			0
$163$	−4.90741			−0.384378			−0.192189	−	0.981358i	$-0.561559\pi$
$163$	−4.90741			−0.384378			−0.192189	+	0.981358i	$0.561559\pi$
$164$		0			0
$165$	5.58231	+	7.22445i	0.434582	+	0.562423i
$166$		0			0
$167$	−1.73832	−	3.01086i	−0.134515	−	0.232987i	0.790897	−	0.611949i	$-0.209614\pi$
$167$	−1.73832	−	3.01086i	−0.134515	−	0.232987i	−0.925412	+	0.378962i	$0.876281\pi$
$168$		0			0
$169$	6.36800	−	11.0297i	0.489846	−	0.848438i
$170$		0			0
$171$	−6.28138	+	24.0909i	−0.480349	+	1.84227i
$172$		0			0
$173$	−5.27114	+	9.12989i	−0.400758	+	0.694133i	−0.993818	−	0.111026i	$-0.964586\pi$
$173$	−5.27114	+	9.12989i	−0.400758	+	0.694133i	0.593060	+	0.805158i	$0.297920\pi$
$174$		0			0
$175$	−1.51859	−	2.63027i	−0.114794	−	0.198830i
$176$		0			0
$177$	−0.497893	+	1.21357i	−0.0374239	+	0.0912177i
$178$		0			0
$179$	4.90741			0.366797			0.183398	−	0.983039i	$-0.441290\pi$
$179$	4.90741			0.366797			0.183398	+	0.983039i	$0.441290\pi$
$180$		0			0
$181$	5.21504			0.387631			0.193816	−	0.981038i	$-0.437914\pi$
$181$	5.21504			0.387631			0.193816	+	0.981038i	$0.437914\pi$
$182$		0			0
$183$	0.465408	−	0.0628686i	0.0344039	−	0.00464738i
$184$		0			0
$185$	3.29408	+	5.70551i	0.242185	+	0.419478i
$186$		0			0
$187$	−7.38804	+	12.7965i	−0.540267	+	0.935770i
$188$		0			0
$189$	1.90160	−	15.6666i	0.138321	−	1.13958i
$190$		0			0
$191$	−12.8451	+	22.2483i	−0.929436	+	1.60983i	−0.145170	+	0.989407i	$0.546373\pi$
$191$	−12.8451	+	22.2483i	−0.929436	+	1.60983i	−0.784267	+	0.620424i	$0.786961\pi$
$192$		0			0
$193$	−1.59840	−	2.76851i	−0.115055	−	0.199282i	0.802747	−	0.596320i	$-0.203371\pi$
$193$	−1.59840	−	2.76851i	−0.115055	−	0.199282i	−0.917802	+	0.397039i	$0.870038\pi$
$194$		0			0
$195$	0.881938	−	0.119135i	0.0631569	−	0.00853141i
$196$		0			0
$197$	13.6808			0.974713			0.487357	−	0.873203i	$-0.337961\pi$
$197$	13.6808			0.974713			0.487357	+	0.873203i	$0.337961\pi$
$198$		0			0
$199$	−5.95413			−0.422077			−0.211039	−	0.977478i	$-0.567685\pi$
$199$	−5.95413			−0.422077			−0.211039	+	0.977478i	$0.567685\pi$
$200$		0			0
$201$	−4.77399	+	11.6362i	−0.336731	+	0.820755i
$202$		0			0
$203$	7.26637	+	12.5857i	0.509999	+	0.883344i
$204$		0			0
$205$	−3.99088	+	6.91240i	−0.278735	+	0.482783i
$206$		0			0
$207$	14.5699	−	4.00945i	1.01268	−	0.278676i
$208$		0			0
$209$	−21.8720	+	37.8834i	−1.51292	+	2.62045i
$210$		0			0
$211$	−7.29408	−	12.6337i	−0.502145	−	0.869741i	−0.999997	−	0.00247872i	$-0.999211\pi$
$211$	−7.29408	−	12.6337i	−0.502145	−	0.869741i	0.497852	−	0.867262i	$-0.334122\pi$
$212$		0			0
$213$	1.57392	+	2.03692i	0.107843	+	0.139567i
$214$		0			0
$215$	−1.19680			−0.0816209
$216$		0			0
$217$	−26.0837			−1.77068
$218$		0			0
$219$	5.63088	+	7.28732i	0.380500	+	0.492432i
$220$		0			0
$221$	0.720159	+	1.24735i	0.0484431	+	0.0839060i
$222$		0			0
$223$	13.8870	−	24.0530i	0.929943	−	1.61071i	0.146531	−	0.989206i	$-0.453189\pi$
$223$	13.8870	−	24.0530i	0.929943	−	1.61071i	0.783412	−	0.621503i	$-0.213477\pi$
$224$		0			0
$225$	−2.13557	−	2.10697i	−0.142371	−	0.140465i
$226$		0			0
$227$	−6.42053	+	11.1207i	−0.426145	+	0.738105i	−0.996527	−	0.0832747i	$-0.973462\pi$
$227$	−6.42053	+	11.1207i	−0.426145	+	0.738105i	0.570381	+	0.821380i	$0.306795\pi$
$228$		0			0
$229$	−12.9530	−	22.4353i	−0.855959	−	1.48256i	−0.875752	−	0.482761i	$-0.839634\pi$
$229$	−12.9530	−	22.4353i	−0.855959	−	1.48256i	0.0197932	−	0.999804i	$-0.493699\pi$
$230$		0			0
$231$	10.5250	−	25.6539i	0.692497	−	1.68790i
$232$		0			0
$233$	5.71998			0.374729			0.187364	−	0.982290i	$-0.440006\pi$
$233$	5.71998			0.374729			0.187364	+	0.982290i	$0.440006\pi$
$234$		0			0
$235$	−9.62533			−0.627887
$236$		0			0
$237$	27.4007	−	3.70137i	1.77987	−	0.240430i
$238$		0			0
$239$	−5.52336	−	9.56674i	−0.357277	−	0.618821i	0.630228	−	0.776410i	$-0.282961\pi$
$239$	−5.52336	−	9.56674i	−0.357277	−	0.618821i	−0.987505	+	0.157589i	$0.949628\pi$
$240$		0			0
$241$	−6.24309	+	10.8134i	−0.402153	+	0.696550i	−0.993986	−	0.109511i	$-0.965071\pi$
$241$	−6.24309	+	10.8134i	−0.402153	+	0.696550i	0.591832	+	0.806061i	$0.298405\pi$
$242$		0			0
$243$	−2.29486	−	15.4186i	−0.147215	−	0.989104i
$244$		0			0
$245$	−1.11221	+	1.92640i	−0.0710565	+	0.123073i
$246$		0			0
$247$	2.13200	+	3.69273i	0.135656	+	0.234963i
$248$		0			0
$249$	−20.7088	+	2.79740i	−1.31236	+	0.177278i
$250$		0			0
$251$	8.22442			0.519121			0.259560	−	0.965727i	$-0.416422\pi$
$251$	8.22442			0.519121			0.259560	+	0.965727i	$0.416422\pi$
$252$		0			0
$253$	26.5517			1.66929
$254$		0			0
$255$	1.84291	−	4.49194i	0.115407	−	0.281296i
$256$		0			0
$257$	−8.41584	−	14.5767i	−0.524966	−	0.909267i	−0.999577	−	0.0290718i	$-0.990745\pi$
$257$	−8.41584	−	14.5767i	−0.524966	−	0.909267i	0.474612	−	0.880195i	$-0.342588\pi$
$258$		0			0
$259$	10.0047	−	17.3286i	0.621661	−	1.07675i
$260$		0			0
$261$	10.2186	+	10.0818i	0.632516	+	0.624046i
$262$		0			0
$263$	−6.06011	+	10.4964i	−0.373682	+	0.647237i	−0.990129	−	0.140160i	$-0.955238\pi$
$263$	−6.06011	+	10.4964i	−0.373682	+	0.647237i	0.616447	+	0.787397i	$0.288572\pi$
$264$		0			0
$265$	0.233971	+	0.405249i	0.0143727	+	0.0248942i
$266$		0			0
$267$	16.1533	+	20.9051i	0.988565	+	1.27937i
$268$		0			0
$269$	−22.5859			−1.37709			−0.688544	−	0.725195i	$-0.741750\pi$
$269$	−22.5859			−1.37709			−0.688544	+	0.725195i	$0.741750\pi$
$270$		0			0
$271$	−10.9818			−0.667094			−0.333547	−	0.942733i	$-0.608246\pi$
$271$	−10.9818			−0.667094			−0.333547	+	0.942733i	$0.608246\pi$
$272$		0			0
$273$	−1.65265	−	2.13882i	−0.100023	−	0.129447i
$274$		0			0
$275$	−2.63557	−	4.56494i	−0.158931	−	0.275276i
$276$		0			0
$277$	−14.3589	+	24.8703i	−0.862741	+	1.49431i	0.00653148	+	0.999979i	$0.497921\pi$
$277$	−14.3589	+	24.8703i	−0.862741	+	1.49431i	−0.869273	+	0.494333i	$0.835412\pi$
$278$		0			0
$279$	−24.8411	+	6.83594i	−1.48720	+	0.409257i
$280$		0			0
$281$	12.1545	−	21.0522i	0.725077	−	1.25587i	−0.233866	−	0.972269i	$-0.575138\pi$
$281$	12.1545	−	21.0522i	0.725077	−	1.25587i	0.958943	−	0.283601i	$-0.0915290\pi$
$282$		0			0
$283$	−7.31224	−	12.6652i	−0.434668	−	0.752866i	0.562601	−	0.826729i	$-0.309801\pi$
$283$	−7.31224	−	12.6652i	−0.434668	−	0.752866i	−0.997268	+	0.0738624i	$0.976467\pi$
$284$		0			0
$285$	5.45586	−	13.2982i	0.323177	−	0.787718i
$286$		0			0
$287$	24.2420			1.43096
$288$		0			0
$289$	−9.14206			−0.537768
$290$		0			0
$291$	10.9231	−	1.47553i	0.640324	−	0.0864968i
$292$		0			0
$293$	−7.84506	−	13.5880i	−0.458314	−	0.793822i	0.540558	−	0.841306i	$-0.318213\pi$
$293$	−7.84506	−	13.5880i	−0.458314	−	0.793822i	−0.998872	+	0.0474842i	$0.984880\pi$
$294$		0			0
$295$	0.378666	−	0.655869i	0.0220468	−	0.0381862i
$296$		0			0
$297$	3.30031	−	27.1901i	0.191503	−	1.57773i
$298$		0			0
$299$	1.29408	−	2.24141i	0.0748385	−	0.129624i
$300$		0			0
$301$	1.81744	+	3.14790i	0.104756	+	0.181442i
$302$		0			0
$303$	3.56053	−	0.480967i	0.204547	−	0.0276309i
$304$		0			0
$305$	−0.271144			−0.0155256
$306$		0			0
$307$	−26.3920			−1.50627			−0.753137	−	0.657864i	$-0.771460\pi$
$307$	−26.3920			−1.50627			−0.753137	+	0.657864i	$0.771460\pi$
$308$		0			0
$309$	3.32403	−	8.10205i	0.189097	−	0.460910i
$310$		0			0
$311$	7.01424	+	12.1490i	0.397741	+	0.688908i	0.993447	−	0.114295i	$-0.0364609\pi$
$311$	7.01424	+	12.1490i	0.397741	+	0.688908i	−0.595706	+	0.803203i	$0.703128\pi$
$312$		0			0
$313$	17.2055	−	29.8008i	0.972511	−	1.68444i	0.284597	−	0.958647i	$-0.408140\pi$
$313$	17.2055	−	29.8008i	0.972511	−	1.68444i	0.687914	−	0.725792i	$-0.258526\pi$
$314$		0			0
$315$	−2.29885	+	8.81675i	−0.129526	+	0.496768i
$316$		0			0
$317$	1.09728	−	1.90055i	0.0616295	−	0.106745i	−0.833564	−	0.552422i	$-0.813704\pi$
$317$	1.09728	−	1.90055i	0.0616295	−	0.106745i	0.895194	+	0.445677i	$0.147037\pi$
$318$		0			0
$319$	12.6111	+	21.8431i	0.706086	+	1.22298i
$320$		0			0
$321$	−14.0746	−	18.2149i	−0.785567	−	1.01666i
$322$		0			0
$323$	23.2631			1.29439
$324$		0			0
$325$	−0.513812			−0.0285011
$326$		0			0
$327$	8.83813	+	11.4380i	0.488750	+	0.632526i
$328$		0			0
$329$	14.6169	+	25.3172i	0.805856	+	1.39578i
$330$		0			0
$331$	−6.44902	+	11.1700i	−0.354470	+	0.613960i	−0.987027	−	0.160554i	$-0.948672\pi$
$331$	−6.44902	+	11.1700i	−0.354470	+	0.613960i	0.632557	+	0.774514i	$0.282005\pi$
$332$		0			0
$333$	4.98661	−	19.1251i	0.273265	−	1.04805i
$334$		0			0
$335$	3.63080	−	6.28872i	0.198372	−	0.343590i
$336$		0			0
$337$	−6.40629	−	11.0960i	−0.348973	−	0.604439i	0.637094	−	0.770786i	$-0.280136\pi$
$337$	−6.40629	−	11.0960i	−0.348973	−	0.604439i	−0.986067	+	0.166347i	$0.946803\pi$
$338$		0			0
$339$	−3.35419	+	8.17556i	−0.182174	+	0.444035i
$340$		0			0
$341$	−45.2694			−2.45148
$342$		0			0
$343$	−14.5043			−0.783157
$344$		0			0
$345$	−8.64611	+	1.16794i	−0.465491	+	0.0628799i
$346$		0			0
$347$	−4.09396	−	7.09095i	−0.219775	−	0.380662i	0.734964	−	0.678106i	$-0.237199\pi$
$347$	−4.09396	−	7.09095i	−0.219775	−	0.380662i	−0.954739	+	0.297444i	$0.903866\pi$
$348$		0			0
$349$	−2.67232	+	4.62859i	−0.143046	+	0.247763i	−0.928642	−	0.370977i	$-0.879023\pi$
$349$	−2.67232	+	4.62859i	−0.143046	+	0.247763i	0.785596	+	0.618739i	$0.212356\pi$
$350$		0			0
$351$	−2.13445	−	1.60380i	−0.113929	−	0.0856044i
$352$		0			0
$353$	7.41584	−	12.8446i	0.394705	−	0.683650i	−0.598358	−	0.801229i	$-0.704180\pi$
$353$	7.41584	−	12.8446i	0.394705	−	0.683650i	0.993064	+	0.117579i	$0.0375134\pi$
$354$		0			0
$355$	−0.743094	−	1.28708i	−0.0394393	−	0.0683110i
$356$		0			0
$357$	−14.6136	+	1.97405i	−0.773435	+	0.104478i
$358$		0			0
$359$	6.55031			0.345712			0.172856	−	0.984947i	$-0.444700\pi$
$359$	6.55031			0.345712			0.172856	+	0.984947i	$0.444700\pi$
$360$		0			0
$361$	49.8695			2.62471
$362$		0			0
$363$	11.0349	−	26.8967i	0.579184	−	1.41171i
$364$		0			0
$365$	−2.65851	−	4.60467i	−0.139153	−	0.241019i
$366$		0			0
$367$	14.0601	−	24.3528i	0.733932	−	1.27121i	−0.221259	−	0.975215i	$-0.571017\pi$
$367$	14.0601	−	24.3528i	0.733932	−	1.27121i	0.955190	−	0.295992i	$-0.0956501\pi$
$368$		0			0
$369$	23.0870	−	6.35326i	1.20186	−	0.330738i
$370$		0			0
$371$	0.710609	−	1.23081i	0.0368930	−	0.0639005i
$372$		0			0
$373$	8.86800	+	15.3598i	0.459168	+	0.795302i	0.998917	−	0.0465241i	$-0.0148144\pi$
$373$	8.86800	+	15.3598i	0.459168	+	0.795302i	−0.539750	+	0.841826i	$0.681481\pi$
$374$		0			0
$375$	1.05903	+	1.37057i	0.0546881	+	0.0707758i
$376$		0			0
$377$	2.45857			0.126623
$378$		0			0
$379$	15.8228			0.812763			0.406381	−	0.913703i	$-0.366790\pi$
$379$	15.8228			0.812763			0.406381	+	0.913703i	$0.366790\pi$
$380$		0			0
$381$	−11.7373	−	15.1900i	−0.601320	−	0.778210i
$382$		0			0
$383$	3.55567	+	6.15861i	0.181686	+	0.314690i	0.942455	−	0.334333i	$-0.108511\pi$
$383$	3.55567	+	6.15861i	0.181686	+	0.314690i	−0.760769	+	0.649023i	$0.775178\pi$
$384$		0			0
$385$	−8.00469	+	13.8645i	−0.407957	+	0.706602i
$386$		0			0
$387$	2.55585	+	2.52162i	0.129921	+	0.128181i
$388$		0			0
$389$	−2.87380	+	4.97757i	−0.145708	+	0.252373i	−0.929637	−	0.368477i	$-0.879879\pi$
$389$	−2.87380	+	4.97757i	−0.145708	+	0.252373i	0.783929	+	0.620850i	$0.213213\pi$
$390$		0			0
$391$	−7.06011	−	12.2285i	−0.357045	−	0.618420i
$392$		0			0
$393$	1.01978	−	2.48563i	0.0514410	−	0.125383i
$394$		0			0
$395$	−15.9635			−0.803211
$396$		0			0
$397$	6.35710			0.319054			0.159527	−	0.987194i	$-0.449003\pi$
$397$	6.35710			0.319054			0.159527	+	0.987194i	$0.449003\pi$
$398$		0			0
$399$	−43.2630	+	5.84410i	−2.16586	+	0.292571i
$400$		0			0
$401$	17.5550	+	30.4061i	0.876654	+	1.51841i	0.854990	+	0.518644i	$0.173563\pi$
$401$	17.5550	+	30.4061i	0.876654	+	1.51841i	0.0216636	+	0.999765i	$0.493104\pi$
$402$		0			0
$403$	−2.20635	+	3.82151i	−0.109906	+	0.190363i
$404$		0			0
$405$	0.121334	+	8.99918i	0.00602913	+	0.447173i
$406$		0			0
$407$	17.3636	−	30.0746i	0.860680	−	1.49074i
$408$		0			0
$409$	−12.4252	−	21.5211i	−0.614387	−	1.06415i	−0.990492	−	0.137573i	$-0.956070\pi$
$409$	−12.4252	−	21.5211i	−0.614387	−	1.06415i	0.376104	−	0.926577i	$-0.377263\pi$
$410$		0			0
$411$	8.26060	−	1.11587i	0.407466	−	0.0550416i
$412$		0			0
$413$	−2.30015			−0.113183
$414$		0			0
$415$	12.0648			0.592238
$416$		0			0
$417$	−14.1122	+	34.3973i	−0.691077	+	1.68444i
$418$		0			0
$419$	−1.68767	−	2.92314i	−0.0824483	−	0.142805i	0.821853	−	0.569700i	$-0.192941\pi$
$419$	−1.68767	−	2.92314i	−0.0824483	−	0.142805i	−0.904301	+	0.426895i	$0.859607\pi$
$420$		0			0
$421$	1.98175	−	3.43250i	0.0965847	−	0.167290i	−0.813684	−	0.581307i	$-0.802541\pi$
$421$	1.98175	−	3.43250i	0.0965847	−	0.167290i	0.910269	+	0.414018i	$0.135875\pi$
$422$		0			0
$423$	20.5556	+	20.2803i	0.999447	+	0.986062i
$424$		0			0
$425$	−1.40160	+	2.42764i	−0.0679876	+	0.117758i
$426$		0			0
$427$	0.411755	+	0.713181i	0.0199262	+	0.0345132i
$428$		0			0
$429$	−2.86825	−	3.71201i	−0.138481	−	0.179217i
$430$		0			0
$431$	7.62516			0.367291			0.183645	−	0.982993i	$-0.441210\pi$
$431$	7.62516			0.367291			0.183645	+	0.982993i	$0.441210\pi$
$432$		0			0
$433$	−7.29024			−0.350347			−0.175173	−	0.984538i	$-0.556049\pi$
$433$	−7.29024			−0.350347			−0.175173	+	0.984538i	$0.556049\pi$
$434$		0			0
$435$	−5.06742	−	6.55810i	−0.242964	−	0.314437i
$436$		0			0
$437$	−20.9012	−	36.2019i	−0.999838	−	1.73177i
$438$		0			0
$439$	−18.1952	+	31.5151i	−0.868411	+	1.50413i	−0.00479205	+	0.999989i	$0.501525\pi$
$439$	−18.1952	+	31.5151i	−0.868411	+	1.50413i	−0.863619	+	0.504144i	$0.831808\pi$
$440$		0			0
$441$	6.43409	−	1.77058i	0.306385	−	0.0843133i
$442$		0			0
$443$	17.6869	−	30.6346i	0.840330	−	1.45549i	−0.0492863	−	0.998785i	$-0.515695\pi$
$443$	17.6869	−	30.6346i	0.840330	−	1.45549i	0.889616	−	0.456709i	$-0.150972\pi$
$444$		0			0
$445$	−7.62645	−	13.2094i	−0.361528	−	0.626185i
$446$		0			0
$447$	−9.72624	+	23.7069i	−0.460035	+	1.12130i
$448$		0			0
$449$	−14.9425			−0.705181			−0.352591	−	0.935778i	$-0.614699\pi$
$449$	−14.9425			−0.705181			−0.352591	+	0.935778i	$0.614699\pi$
$450$		0			0
$451$	42.0730			1.98114
$452$		0			0
$453$	−1.68514	+	0.227634i	−0.0791748	+	0.0106952i
$454$		0			0
$455$	0.780267	+	1.35146i	0.0365795	+	0.0633575i
$456$		0			0
$457$	6.39205	−	11.0714i	0.299008	−	0.517896i	−0.676902	−	0.736074i	$-0.736678\pi$
$457$	6.39205	−	11.0714i	0.299008	−	0.517896i	0.975909	+	0.218177i	$0.0700111\pi$
$458$		0			0
$459$	−13.4001	+	5.70990i	−0.625461	+	0.266515i
$460$		0			0
$461$	−4.05722	+	7.02730i	−0.188963	+	0.327294i	−0.944905	−	0.327345i	$-0.893846\pi$
$461$	−4.05722	+	7.02730i	−0.188963	+	0.327294i	0.755942	+	0.654639i	$0.227179\pi$
$462$		0			0
$463$	10.7803	+	18.6720i	0.501002	+	0.867760i	0.999999	+	0.00115683i	$0.000368231\pi$
$463$	10.7803	+	18.6720i	0.501002	+	0.867760i	−0.498998	+	0.866603i	$0.666298\pi$
$464$		0			0
$465$	14.7412	−	1.99129i	0.683609	−	0.0923439i
$466$		0			0
$467$	−30.8602			−1.42804			−0.714019	−	0.700127i	$-0.753127\pi$
$467$	−30.8602			−1.42804			−0.714019	+	0.700127i	$0.753127\pi$
$468$		0			0
$469$	−22.0547			−1.01839
$470$		0			0
$471$	−4.51098	+	10.9951i	−0.207855	+	0.506629i
$472$		0			0
$473$	3.15425	+	5.46331i	0.145032	+	0.251203i
$474$		0			0
$475$	−4.14938	+	7.18694i	−0.190387	+	0.329760i
$476$		0			0
$477$	0.354187	−	1.35841i	0.0162171	−	0.0621972i
$478$		0			0
$479$	0.532059	−	0.921553i	0.0243104	−	0.0421068i	−0.853614	−	0.520906i	$-0.825594\pi$
$479$	0.532059	−	0.921553i	0.0243104	−	0.0421068i	0.877925	+	0.478799i	$0.158928\pi$
$480$		0			0
$481$	−1.69254	−	2.93156i	−0.0771730	−	0.133668i
$482$		0			0
$483$	16.2019	+	20.9680i	0.737211	+	0.954076i
$484$		0			0
$485$	−6.36374			−0.288962
$486$		0			0
$487$	−27.0182			−1.22431			−0.612157	−	0.790736i	$-0.709698\pi$
$487$	−27.0182			−1.22431			−0.612157	+	0.790736i	$0.709698\pi$
$488$		0			0
$489$	−5.19710	−	6.72593i	−0.235021	−	0.304157i
$490$		0			0
$491$	−8.11690	−	14.0589i	−0.366310	−	0.634468i	0.622675	−	0.782481i	$-0.286046\pi$
$491$	−8.11690	−	14.0589i	−0.366310	−	0.634468i	−0.988986	+	0.148012i	$0.952713\pi$
$492$		0			0
$493$	6.70660	−	11.6162i	0.302050	−	0.523166i
$494$		0			0
$495$	−3.98976	+	15.3018i	−0.179326	+	0.687767i
$496$		0			0
$497$	−2.25691	+	3.90908i	−0.101236	+	0.175346i
$498$		0			0
$499$	−10.3604	−	17.9448i	−0.463796	−	0.803318i	0.535350	−	0.844630i	$-0.320180\pi$
$499$	−10.3604	−	17.9448i	−0.463796	−	0.803318i	−0.999146	+	0.0413119i	$0.986846\pi$
$500$		0			0
$501$	2.28565	−	5.57107i	0.102115	−	0.248897i
$502$		0			0
$503$	−5.47834			−0.244267			−0.122134	−	0.992514i	$-0.538974\pi$
$503$	−5.47834			−0.244267			−0.122134	+	0.992514i	$0.538974\pi$
$504$		0			0
$505$	−2.07435			−0.0923072
$506$		0			0
$507$	21.8608	−	2.95303i	0.970874	−	0.131149i
$508$		0			0
$509$	4.35530	+	7.54361i	0.193045	+	0.334365i	0.946258	−	0.323413i	$-0.104830\pi$
$509$	4.35530	+	7.54361i	0.193045	+	0.334365i	−0.753213	+	0.657777i	$0.771497\pi$
$510$		0			0
$511$	−8.07435	+	13.9852i	−0.357188	+	0.618668i
$512$		0			0
$513$	−39.6703	+	16.9039i	−1.75149	+	0.746327i
$514$		0			0
$515$	−2.52805	+	4.37871i	−0.111399	+	0.192949i
$516$		0			0
$517$	25.3683	+	43.9391i	1.11569	+	1.93244i
$518$		0			0
$519$	−18.0954	+	2.44438i	−0.794301	+	0.107297i
$520$		0			0
$521$	−2.87041			−0.125755			−0.0628774	−	0.998021i	$-0.520028\pi$
$521$	−2.87041			−0.125755			−0.0628774	+	0.998021i	$0.520028\pi$
$522$		0			0
$523$	−6.65295			−0.290913			−0.145457	−	0.989365i	$-0.546465\pi$
$523$	−6.65295			−0.290913			−0.145457	+	0.989365i	$0.546465\pi$
$524$		0			0
$525$	1.99673	−	4.86686i	0.0871444	−	0.212407i
$526$		0			0
$527$	12.0372	+	20.8490i	0.524347	+	0.908197i
$528$		0			0
$529$	−1.18656	+	2.05518i	−0.0515894	+	0.0893555i
$530$		0			0
$531$	−2.19057	+	0.602816i	−0.0950625	+	0.0261600i
$532$		0			0
$533$	2.05056	−	3.55167i	0.0888195	−	0.153840i
$534$		0			0
$535$	6.64503	+	11.5095i	0.287290	+	0.497601i
$536$		0			0
$537$	5.19710	+	6.72593i	0.224271	+	0.290245i
$538$		0			0
$539$	11.7252			0.505042
$540$		0			0
$541$	7.79348			0.335068			0.167534	−	0.985866i	$-0.446420\pi$
$541$	7.79348			0.335068			0.167534	+	0.985866i	$0.446420\pi$
$542$		0			0
$543$	5.52290	+	7.14757i	0.237010	+	0.306731i
$544$		0			0
$545$	−4.17274	−	7.22741i	−0.178741	−	0.309588i
$546$		0			0
$547$	5.87901	−	10.1827i	0.251368	−	0.435382i	−0.712535	−	0.701637i	$-0.752453\pi$
$547$	5.87901	−	10.1827i	0.251368	−	0.435382i	0.963903	+	0.266255i	$0.0857862\pi$
$548$		0			0
$549$	0.579047	+	0.571292i	0.0247131	+	0.0243822i
$550$		0			0
$551$	19.8546	−	34.3892i	0.845835	−	1.46503i
$552$		0			0
$553$	24.2420	+	41.9883i	1.03087	+	1.78552i
$554$		0			0
$555$	−4.33125	+	10.5571i	−0.183851	+	0.448123i
$556$		0			0
$557$	16.7827			0.711107			0.355553	−	0.934656i	$-0.384292\pi$
$557$	16.7827			0.711107			0.355553	+	0.934656i	$0.384292\pi$
$558$		0			0
$559$	0.614928			0.0260087
$560$		0			0
$561$	−25.3626	+	3.42605i	−1.07081	+	0.144648i
$562$		0			0
$563$	12.8743	+	22.2990i	0.542588	+	0.939790i	0.998754	+	0.0498953i	$0.0158887\pi$
$563$	12.8743	+	22.2990i	0.542588	+	0.939790i	−0.456167	+	0.889894i	$0.650778\pi$
$564$		0			0
$565$	2.55098	−	4.41844i	0.107321	−	0.185885i
$566$		0			0
$567$	23.4860	−	13.9852i	0.986320	−	0.587322i
$568$		0			0
$569$	2.55654	−	4.42805i	0.107176	−	0.185634i	−0.807449	−	0.589937i	$-0.799153\pi$
$569$	2.55654	−	4.42805i	0.107176	−	0.185634i	0.914625	+	0.404303i	$0.132486\pi$
$570$		0			0
$571$	−12.7329	−	22.0539i	−0.532853	−	0.922929i	−0.999264	−	0.0383607i	$-0.987786\pi$
$571$	−12.7329	−	22.0539i	−0.532853	−	0.922929i	0.466411	−	0.884568i	$-0.345547\pi$
$572$		0			0
$573$	−44.0961	+	5.95663i	−1.84214	+	0.248842i
$574$		0			0
$575$	5.03717			0.210065
$576$		0			0
$577$	44.7164			1.86157			0.930783	−	0.365571i	$-0.119126\pi$
$577$	44.7164			1.86157			0.930783	+	0.365571i	$0.119126\pi$
$578$		0			0
$579$	2.10167	−	5.12265i	0.0873424	−	0.212890i
$580$		0			0
$581$	−18.3214	−	31.7337i	−0.760101	−	1.31653i
$582$		0			0
$583$	1.23329	−	2.13612i	0.0510777	−	0.0884692i
$584$		0			0
$585$	1.09728	+	1.08259i	0.0453670	+	0.0447595i
$586$		0			0
$587$	20.4578	−	35.4339i	0.844383	−	1.46251i	−0.0417725	−	0.999127i	$-0.513300\pi$
$587$	20.4578	−	35.4339i	0.844383	−	1.46251i	0.886156	−	0.463388i	$-0.153366\pi$
$588$		0			0
$589$	35.6356	+	61.7226i	1.46834	+	2.54324i
$590$		0			0
$591$	14.4883	+	18.7504i	0.595971	+	0.771288i
$592$		0			0
$593$	−11.9729			−0.491667			−0.245834	−	0.969312i	$-0.579062\pi$
$593$	−11.9729			−0.491667			−0.245834	+	0.969312i	$0.579062\pi$
$594$		0			0
$595$	8.51381			0.349032
$596$		0			0
$597$	−6.30561	−	8.16053i	−0.258071	−	0.333988i
$598$		0			0
$599$	−7.17855	−	12.4336i	−0.293308	−	0.508024i	0.681282	−	0.732021i	$-0.261423\pi$
$599$	−7.17855	−	12.4336i	−0.293308	−	0.508024i	−0.974590	+	0.223997i	$0.928089\pi$
$600$		0			0
$601$	−22.3210	+	38.6611i	−0.910493	+	1.57702i	−0.0971239	+	0.995272i	$0.530964\pi$
$601$	−22.3210	+	38.6611i	−0.910493	+	1.57702i	−0.813369	+	0.581748i	$0.802369\pi$
$602$		0			0
$603$	−21.0040	+	5.78003i	−0.855349	+	0.235381i
$604$		0			0
$605$	−8.39248	+	14.5362i	−0.341203	+	0.590980i
$606$		0			0
$607$	14.8870	+	25.7851i	0.604245	+	1.04658i	0.992170	+	0.124892i	$0.0398586\pi$
$607$	14.8870	+	25.7851i	0.604245	+	1.04658i	−0.387925	+	0.921691i	$0.626808\pi$
$608$		0			0
$609$	−9.55426	+	23.2877i	−0.387158	+	0.943666i
$610$		0			0
$611$	4.94561			0.200078
$612$		0			0
$613$	33.4132			1.34955			0.674773	−	0.738025i	$-0.264241\pi$
$613$	33.4132			1.34955			0.674773	+	0.738025i	$0.264241\pi$
$614$		0			0
$615$	−13.7004	+	1.85069i	−0.552452	+	0.0746269i
$616$		0			0
$617$	22.2941	+	38.6145i	0.897525	+	1.55456i	0.830648	+	0.556798i	$0.187970\pi$
$617$	22.2941	+	38.6145i	0.897525	+	1.55456i	0.0668776	+	0.997761i	$0.478696\pi$
$618$		0			0
$619$	18.4766	−	32.0025i	0.742638	−	1.28629i	−0.208652	−	0.977990i	$-0.566908\pi$
$619$	18.4766	−	32.0025i	0.742638	−	1.28629i	0.951290	−	0.308297i	$-0.0997591\pi$
$620$		0			0
$621$	20.9252	+	15.7229i	0.839700	+	0.630938i
$622$		0			0
$623$	−23.1628	+	40.1192i	−0.928000	+	1.60734i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−75.0849	+	10.1427i	−2.99860	+	0.405060i
$628$		0			0
$629$	−18.4679			−0.736365
$630$		0			0
$631$	−1.10197			−0.0438687			−0.0219344	−	0.999759i	$-0.506982\pi$
$631$	−1.10197			−0.0438687			−0.0219344	+	0.999759i	$0.506982\pi$
$632$		0			0
$633$	9.59069	−	23.3765i	0.381196	−	0.929133i
$634$		0			0
$635$	5.54152	+	9.59820i	0.219909	+	0.380893i
$636$		0			0
$637$	0.571466	−	0.989809i	0.0226423	−	0.0392177i
$638$		0			0
$639$	−1.12490	+	4.31432i	−0.0445005	+	0.170672i
$640$		0			0
$641$	6.78453	−	11.7511i	0.267973	−	0.464142i	−0.700365	−	0.713784i	$-0.746980\pi$
$641$	6.78453	−	11.7511i	0.267973	−	0.464142i	0.968338	+	0.249642i	$0.0803129\pi$
$642$		0			0
$643$	−4.86477	−	8.42602i	−0.191848	−	0.332290i	0.754015	−	0.656857i	$-0.228115\pi$
$643$	−4.86477	−	8.42602i	−0.191848	−	0.332290i	−0.945863	+	0.324567i	$0.894781\pi$
$644$		0			0
$645$	−1.26745	−	1.64029i	−0.0499056	−	0.0645864i
$646$		0			0
$647$	−38.5786			−1.51668			−0.758341	−	0.651858i	$-0.773990\pi$
$647$	−38.5786			−1.51668			−0.758341	+	0.651858i	$0.773990\pi$
$648$		0			0
$649$	−3.99201			−0.156700
$650$		0			0
$651$	−27.6235	−	35.7495i	−1.08265	−	1.40113i
$652$		0			0
$653$	−8.56522	−	14.8354i	−0.335183	−	0.580554i	0.648337	−	0.761354i	$-0.275465\pi$
$653$	−8.56522	−	14.8354i	−0.335183	−	0.580554i	−0.983520	+	0.180799i	$0.942132\pi$
$654$		0			0
$655$	−0.775579	+	1.34334i	−0.0303044	+	0.0524888i
$656$		0			0
$657$	−4.02448	+	15.4350i	−0.157010	+	0.602177i
$658$		0			0
$659$	11.8315	−	20.4928i	0.460890	−	0.798285i	−0.538116	−	0.842871i	$-0.680864\pi$
$659$	11.8315	−	20.4928i	0.460890	−	0.798285i	0.999006	+	0.0445862i	$0.0141969\pi$
$660$		0			0
$661$	−9.21504	−	15.9609i	−0.358424	−	0.620808i	0.629274	−	0.777184i	$-0.283352\pi$
$661$	−9.21504	−	15.9609i	−0.358424	−	0.620808i	−0.987698	+	0.156375i	$0.950019\pi$
$662$		0			0
$663$	−0.946908	+	2.30801i	−0.0367749	+	0.0896357i
$664$		0			0
$665$	25.2048			0.977400
$666$		0			0
$667$	−24.1026			−0.933258
$668$		0			0
$669$	47.6730	−	6.43981i	1.84315	−	0.248978i
$670$		0			0
$671$	0.714619	+	1.23776i	0.0275875	+	0.0477830i
$672$		0			0
$673$	8.24821	−	14.2863i	0.317945	−	0.550697i	−0.662114	−	0.749403i	$-0.730341\pi$
$673$	8.24821	−	14.2863i	0.317945	−	0.550697i	0.980059	+	0.198706i	$0.0636739\pi$
$674$		0			0
$675$	0.626109	−	5.15829i	0.0240989	−	0.198543i
$676$		0			0
$677$	−5.05141	+	8.74930i	−0.194141	+	0.336263i	−0.946619	−	0.322355i	$-0.895525\pi$
$677$	−5.05141	+	8.74930i	−0.194141	+	0.336263i	0.752477	+	0.658618i	$0.228859\pi$
$678$		0			0
$679$	9.66389	+	16.7383i	0.370866	+	0.642359i
$680$		0			0
$681$	−22.0412	+	2.97739i	−0.844619	+	0.114094i
$682$		0			0
$683$	−8.16917			−0.312585			−0.156292	−	0.987711i	$-0.549954\pi$
$683$	−8.16917			−0.312585			−0.156292	+	0.987711i	$0.549954\pi$
$684$		0			0
$685$	−4.81258			−0.183879
$686$		0			0
$687$	17.0314	−	41.5126i	0.649788	−	1.58381i
$688$		0			0
$689$	−0.120217	−	0.208222i	−0.00457989	−	0.00793261i
$690$		0			0
$691$	1.75733	−	3.04379i	0.0668521	−	0.115791i	−0.830662	−	0.556777i	$-0.812038\pi$
$691$	1.75733	−	3.04379i	0.0668521	−	0.115791i	0.897514	+	0.440986i	$0.145371\pi$
$692$		0			0
$693$	46.3068	−	12.7430i	1.75905	−	0.484068i
$694$		0			0
$695$	10.7329	−	18.5898i	0.407120	−	0.705153i
$696$		0			0
$697$	−11.1872	−	19.3769i	−0.423747	−	0.733951i
$698$		0			0
$699$	6.05764	+	7.83962i	0.229121	+	0.296522i
$700$		0			0
$701$	33.9897			1.28378			0.641888	−	0.766799i	$-0.278152\pi$
$701$	33.9897			1.28378			0.641888	+	0.766799i	$0.278152\pi$
$702$		0			0
$703$	−54.6736			−2.06205
$704$		0			0
$705$	−10.1935	−	13.1922i	−0.383910	−	0.496845i
$706$		0			0
$707$	3.15007	+	5.45609i	0.118471	+	0.205197i
$708$		0			0
$709$	1.99888	−	3.46217i	0.0750696	−	0.130024i	−0.826047	−	0.563601i	$-0.809415\pi$
$709$	1.99888	−	3.46217i	0.0750696	−	0.130024i	0.901117	+	0.433577i	$0.142749\pi$
$710$		0			0
$711$	34.0912	+	33.6347i	1.27852	+	1.26140i
$712$		0			0
$713$	21.6300	−	37.4643i	0.810051	−	1.40305i
$714$		0			0
$715$	1.35419	+	2.34552i	0.0506437	+	0.0877175i
$716$		0			0
$717$	7.26245	−	17.7016i	0.271221	−	0.661079i
$718$		0			0
$719$	−33.2142			−1.23868			−0.619340	−	0.785123i	$-0.712600\pi$
$719$	−33.2142			−1.23868			−0.619340	+	0.785123i	$0.712600\pi$
$720$		0			0
$721$	15.3562			0.571897
$722$		0			0
$723$	−21.4321	+	2.89511i	−0.797067	+	0.107670i
$724$		0			0
$725$	2.39248	+	4.14389i	0.0888544	+	0.153900i
$726$		0			0
$727$	13.7944	−	23.8926i	0.511607	−	0.886129i	−0.488303	−	0.872674i	$-0.662384\pi$
$727$	13.7944	−	23.8926i	0.511607	−	0.886129i	0.999909	−	0.0134545i	$-0.00428282\pi$
$728$		0			0
$729$	18.7019	−	19.4740i	0.692663	−	0.721261i
$730$		0			0
$731$	1.67743	−	2.90540i	0.0620421	−	0.107460i
$732$		0			0
$733$	−4.85930	−	8.41656i	−0.179482	−	0.310873i	0.762221	−	0.647317i	$-0.224109\pi$
$733$	−4.85930	−	8.41656i	−0.179482	−	0.310873i	−0.941703	+	0.336444i	$0.890776\pi$
$734$		0			0
$735$	−3.81813	+	0.515764i	−0.140834	+	0.0190243i
$736$		0			0
$737$	−38.2769			−1.40995
$738$		0			0
$739$	36.2355			1.33294			0.666472	−	0.745530i	$-0.267803\pi$
$739$	36.2355			1.33294			0.666472	+	0.745530i	$0.267803\pi$
$740$		0			0
$741$	−2.80328	+	6.83277i	−0.102981	+	0.251008i
$742$		0			0
$743$	−10.3407	−	17.9106i	−0.379364	−	0.657078i	0.611606	−	0.791163i	$-0.290524\pi$
$743$	−10.3407	−	17.9106i	−0.379364	−	0.657078i	−0.990970	+	0.134085i	$0.957191\pi$
$744$		0			0
$745$	7.39717	−	12.8123i	0.271011	−	0.469405i
$746$		0			0
$747$	−25.7652	−	25.4202i	−0.942701	−	0.930076i
$748$		0			0
$749$	20.1821	−	34.9565i	0.737439	−	1.27728i
$750$		0			0
$751$	−14.5374	−	25.1796i	−0.530478	−	0.918815i	−0.999368	−	0.0355583i	$-0.988679\pi$
$751$	−14.5374	−	25.1796i	−0.530478	−	0.918815i	0.468889	−	0.883257i	$-0.344654\pi$
$752$		0			0
$753$	8.70992	+	11.2721i	0.317407	+	0.410779i
$754$		0			0
$755$	0.981753			0.0357296
$756$		0			0
$757$	−22.1202			−0.803973			−0.401986	−	0.915646i	$-0.631680\pi$
$757$	−22.1202			−0.803973			−0.401986	+	0.915646i	$0.631680\pi$
$758$		0			0
$759$	28.1190	+	36.3908i	1.02066	+	1.32090i
$760$		0			0
$761$	−7.64537	−	13.2422i	−0.277145	−	0.480029i	0.693529	−	0.720428i	$-0.256055\pi$
$761$	−7.64537	−	13.2422i	−0.277145	−	0.480029i	−0.970674	+	0.240400i	$0.922721\pi$
$762$		0			0
$763$	−12.6733	+	21.9509i	−0.458806	+	0.794675i
$764$		0			0
$765$	8.10820	−	2.23127i	0.293153	−	0.0806719i
$766$		0			0
$767$	−0.194563	+	0.336993i	−0.00702526	+	0.0121681i
$768$		0			0
$769$	−13.9989	−	24.2468i	−0.504813	−	0.874361i	−0.999985	−	0.00556608i	$-0.998228\pi$
$769$	−13.9989	−	24.2468i	−0.504813	−	0.874361i	0.495172	−	0.868795i	$-0.335105\pi$
$770$		0			0
$771$	11.0656	−	26.9716i	0.398520	−	0.971359i
$772$		0			0
$773$	−18.4853			−0.664871			−0.332436	−	0.943126i	$-0.607870\pi$
$773$	−18.4853			−0.664871			−0.332436	+	0.943126i	$0.607870\pi$
$774$		0			0
$775$	−8.58816			−0.308496
$776$		0			0
$777$	34.3453	−	4.63947i	1.23213	−	0.166440i
$778$		0			0
$779$	−33.1194	−	57.3644i	−1.18662	−	2.05529i
$780$		0			0
$781$	−3.91696	+	6.78437i	−0.140160	+	0.242764i
$782$		0			0
$783$	−2.99590	+	24.6822i	−0.107065	+	0.882070i
$784$		0			0
$785$	3.43077	−	5.94226i	0.122449	−	0.212089i
$786$		0			0
$787$	−4.46308	−	7.73028i	−0.159092	−	0.275555i	0.775450	−	0.631409i	$-0.217523\pi$
$787$	−4.46308	−	7.73028i	−0.159092	−	0.275555i	−0.934541	+	0.355855i	$0.884190\pi$
$788$		0			0
$789$	−20.8039	+	2.81025i	−0.740638	+	0.100048i
$790$		0			0
$791$	−15.4956			−0.550959
$792$		0			0
$793$	0.139317			0.00494728
$794$		0			0
$795$	−0.307638	+	0.749843i	−0.0109108	+	0.0265942i
$796$		0			0
$797$	16.2277	+	28.1072i	0.574816	+	0.995610i	0.996062	+	0.0886634i	$0.0282595\pi$
$797$	16.2277	+	28.1072i	0.574816	+	0.995610i	−0.421246	+	0.906946i	$0.638407\pi$
$798$		0			0
$799$	13.4909	−	23.3669i	0.477273	−	0.826661i
$800$		0			0
$801$	−11.5450	+	44.2783i	−0.407923	+	1.56450i
$802$		0			0
$803$	−14.0134	+	24.2719i	−0.494521	+	0.856536i
$804$		0			0
$805$	−7.64938	−	13.2491i	−0.269605	−	0.466970i
$806$		0			0
$807$	−23.9192	−	30.9555i	−0.841996	−	1.08969i
$808$		0			0
$809$	12.4759			0.438631			0.219315	−	0.975654i	$-0.429618\pi$
$809$	12.4759			0.438631			0.219315	+	0.975654i	$0.429618\pi$
$810$		0			0
$811$	−16.0632			−0.564057			−0.282028	−	0.959406i	$-0.591007\pi$
$811$	−16.0632			−0.564057			−0.282028	+	0.959406i	$0.591007\pi$
$812$		0			0
$813$	−11.6300	−	15.0512i	−0.407883	−	0.527869i
$814$		0			0
$815$	2.45370	+	4.24994i	0.0859495	+	0.148869i
$816$		0			0
$817$	4.96597	−	8.60131i	0.173737	−	0.300922i
$818$		0			0
$819$	1.18118	−	4.53015i	0.0412737	−	0.158296i
$820$		0			0
$821$	−23.8075	+	41.2357i	−0.830886	+	1.43914i	0.0664509	+	0.997790i	$0.478832\pi$
$821$	−23.8075	+	41.2357i	−0.830886	+	1.43914i	−0.897337	+	0.441347i	$0.854501\pi$
$822$		0			0
$823$	−8.87764	−	15.3765i	−0.309455	−	0.535992i	0.668788	−	0.743453i	$-0.266813\pi$
$823$	−8.87764	−	15.3765i	−0.309455	−	0.535992i	−0.978243	+	0.207461i	$0.933480\pi$
$824$		0			0
$825$	3.46541	−	8.44665i	0.120650	−	0.294074i
$826$		0			0
$827$	24.2420			0.842976			0.421488	−	0.906834i	$-0.361508\pi$
$827$	24.2420			0.842976			0.421488	+	0.906834i	$0.361508\pi$
$828$		0			0
$829$	−30.3816			−1.05520			−0.527599	−	0.849494i	$-0.676908\pi$
$829$	−30.3816			−1.05520			−0.527599	+	0.849494i	$0.676908\pi$
$830$		0			0
$831$	−49.2929	+	6.65863i	−1.70995	+	0.230985i
$832$		0			0
$833$	−3.11775	−	5.40010i	−0.108024	−	0.187102i
$834$		0			0
$835$	−1.73832	+	3.01086i	−0.0601570	+	0.104195i
$836$		0			0
$837$	−35.6766	−	26.8068i	−1.23316	−	0.926580i
$838$		0			0
$839$	5.32170	−	9.21746i	0.183726	−	0.318222i	−0.759421	−	0.650600i	$-0.774518\pi$
$839$	5.32170	−	9.21746i	0.183726	−	0.318222i	0.943146	+	0.332378i	$0.107851\pi$
$840$		0			0
$841$	3.05210	+	5.28640i	0.105245	+	0.182290i
$842$		0			0
$843$	41.7254	−	5.63640i	1.43710	−	0.194128i
$844$		0			0
$845$	−12.7360			−0.438132
$846$		0			0
$847$	50.9788			1.75165
$848$		0			0
$849$	9.61457	−	23.4347i	0.329971	−	0.804278i
$850$		0			0
$851$	16.5928	+	28.7397i	0.568795	+	0.985183i
$852$		0			0
$853$	−13.5746	+	23.5119i	−0.464785	+	0.805032i	−0.999192	−	0.0401957i	$-0.987202\pi$
$853$	−13.5746	+	23.5119i	−0.464785	+	0.805032i	0.534406	+	0.845228i	$0.320535\pi$
$854$		0			0
$855$	24.0040	−	6.60560i	0.820919	−	0.225907i
$856$		0			0
$857$	−21.5833	+	37.3834i	−0.737271	+	1.27699i	0.216448	+	0.976294i	$0.430553\pi$
$857$	−21.5833	+	37.3834i	−0.737271	+	1.27699i	−0.953720	+	0.300697i	$0.902781\pi$
$858$		0			0
$859$	3.30986	+	5.73285i	0.112931	+	0.195602i	0.916951	−	0.399000i	$-0.130643\pi$
$859$	3.30986	+	5.73285i	0.112931	+	0.195602i	−0.804020	+	0.594603i	$0.797309\pi$
$860$		0			0
$861$	25.6730	+	33.2252i	0.874933	+	1.13231i
$862$		0			0
$863$	5.31055			0.180773			0.0903866	−	0.995907i	$-0.471190\pi$
$863$	5.31055			0.180773			0.0903866	+	0.995907i	$0.471190\pi$
$864$		0			0
$865$	10.5423			0.358449
$866$		0			0
$867$	−9.68172	−	12.5298i	−0.328809	−	0.425534i
$868$		0			0
$869$	42.0730	+	72.8725i	1.42723	+	2.47203i
$870$		0			0
$871$	−1.86555	+	3.23122i	−0.0632116	+	0.109486i
$872$		0			0
$873$	13.5902	+	13.4082i	0.459959	+	0.453799i
$874$		0			0
$875$	−1.51859	+	2.63027i	−0.0513376	+	0.0889193i
$876$		0			0
$877$	1.06011	+	1.83616i	0.0357973	+	0.0620028i	0.883369	−	0.468678i	$-0.155270\pi$
$877$	1.06011	+	1.83616i	0.0357973	+	0.0620028i	−0.847572	+	0.530681i	$0.821936\pi$
$878$		0			0
$879$	10.3152	−	25.1424i	0.347922	−	0.848030i
$880$		0			0
$881$	22.5668			0.760296			0.380148	−	0.924926i	$-0.375873\pi$
$881$	22.5668			0.760296			0.380148	+	0.924926i	$0.375873\pi$
$882$		0			0
$883$	41.5399			1.39793			0.698964	−	0.715157i	$-0.253645\pi$
$883$	41.5399			1.39793			0.698964	+	0.715157i	$0.253645\pi$
$884$		0			0
$885$	1.29993	−	0.175599i	0.0436967	−	0.00590268i
$886$		0			0
$887$	21.7248	+	37.6285i	0.729449	+	1.26344i	0.957116	+	0.289704i	$0.0935568\pi$
$887$	21.7248	+	37.6285i	0.729449	+	1.26344i	−0.227667	+	0.973739i	$0.573110\pi$
$888$		0			0
$889$	16.8306	−	29.1514i	0.564479	−	0.977706i
$890$		0			0
$891$	40.7610	−	24.2719i	1.36554	−	0.813138i
$892$		0			0
$893$	39.9392	−	69.1767i	1.33651	−	2.31491i
$894$		0			0
$895$	−2.45370	−	4.24994i	−0.0820183	−	0.142060i
$896$		0			0
$897$	4.44247	−	0.600102i	0.148330	−	0.0200368i
$898$		0			0
$899$	41.0940			1.37056
$900$		0			0
$901$	−1.31173			−0.0437002
$902$		0			0
$903$	−2.38968	+	5.82465i	−0.0795236	+	0.193832i
$904$		0			0
$905$	−2.60752	−	4.51636i	−0.0866770	−	0.150129i
$906$		0			0
$907$	−2.19133	+	3.79550i	−0.0727620	+	0.126027i	−0.900111	−	0.435661i	$-0.856515\pi$
$907$	−2.19133	+	3.79550i	−0.0727620	+	0.126027i	0.827349	+	0.561688i	$0.189848\pi$
$908$		0			0
$909$	4.42992	+	4.37059i	0.146931	+	0.144963i
$910$		0			0
$911$	−7.33594	+	12.7062i	−0.243051	+	0.420976i	−0.961582	−	0.274519i	$-0.911481\pi$
$911$	−7.33594	+	12.7062i	−0.243051	+	0.420976i	0.718531	+	0.695495i	$0.244815\pi$
$912$		0			0
$913$	−31.7976	−	55.0751i	−1.05235	−	1.82272i
$914$		0			0
$915$	−0.287150	−	0.371620i	−0.00949287	−	0.0122854i
$916$		0			0
$917$	4.71114			0.155575
$918$		0			0
$919$	−37.3233			−1.23118			−0.615591	−	0.788066i	$-0.711083\pi$
$919$	−37.3233			−1.23118			−0.615591	+	0.788066i	$0.711083\pi$
$920$		0			0
$921$	−27.9500	−	36.1720i	−0.920984	−	1.19191i
$922$		0			0
$923$	0.381810	+	0.661315i	0.0125674	+	0.0217674i
$924$		0			0
$925$	3.29408	−	5.70551i	0.108309	−	0.187596i
$926$		0			0
$927$	14.6247	−	4.02452i	0.480337	−	0.132183i
$928$		0			0
$929$	9.66250	−	16.7359i	0.317016	−	0.549089i	−0.662848	−	0.748754i	$-0.730652\pi$
$929$	9.66250	−	16.7359i	0.317016	−	0.549089i	0.979864	+	0.199666i	$0.0639856\pi$
$930$		0			0
$931$	−9.22997	−	15.9868i	−0.302500	−	0.523946i
$932$		0			0
$933$	−9.22274	+	22.4797i	−0.301939	+	0.735951i
$934$		0			0
$935$	14.7761			0.483230
$936$		0			0
$937$	−15.8339			−0.517271			−0.258636	−	0.965975i	$-0.583273\pi$
$937$	−15.8339			−0.517271			−0.258636	+	0.965975i	$0.583273\pi$
$938$		0			0
$939$	59.0651	−	7.97869i	1.92752	−	0.260375i
$940$		0			0
$941$	2.17967	+	3.77529i	0.0710551	+	0.123071i	0.899364	−	0.437201i	$-0.144030\pi$
$941$	2.17967	+	3.77529i	0.0710551	+	0.123071i	−0.828309	+	0.560272i	$0.810697\pi$
$942$		0			0
$943$	−20.1027	+	34.8190i	−0.654635	+	1.13386i
$944$		0			0
$945$	−14.5185	+	6.18648i	−0.472287	+	0.201246i
$946$		0			0
$947$	−19.8158	+	34.3220i	−0.643927	+	1.11531i	0.340621	+	0.940201i	$0.389363\pi$
$947$	−19.8158	+	34.3220i	−0.643927	+	1.11531i	−0.984548	+	0.175114i	$0.943971\pi$
$948$		0			0
$949$	1.36597	+	2.36593i	0.0443413	+	0.0768014i
$950$		0			0
$951$	3.76688	−	0.508842i	0.122150	−	0.0165003i
$952$		0			0
$953$	−38.3922			−1.24365			−0.621823	−	0.783158i	$-0.713608\pi$
$953$	−38.3922			−1.24365			−0.621823	+	0.783158i	$0.713608\pi$
$954$		0			0
$955$	25.6901			0.831313
$956$		0			0
$957$	−16.5818	+	40.4168i	−0.536014	+	1.30649i
$958$		0			0
$959$	7.30832	+	12.6584i	0.235998	+	0.408760i
$960$		0			0
$961$	−21.3782	+	37.0282i	−0.689620	+	1.19446i
$962$		0			0
$963$	10.0593	−	38.5803i	0.324157	−	1.24323i
$964$		0			0
$965$	−1.59840	+	2.76851i	−0.0514543	+	0.0891214i
$966$		0			0
$967$	26.1628	+	45.3154i	0.841340	+	1.45724i	0.888762	+	0.458369i	$0.151566\pi$
$967$	26.1628	+	45.3154i	0.841340	+	1.45724i	−0.0474216	+	0.998875i	$0.515100\pi$
$968$		0			0
$969$	24.6364	+	31.8837i	0.791434	+	1.02425i
$970$		0			0
$971$	−45.4831			−1.45962			−0.729811	−	0.683649i	$-0.760392\pi$
$971$	−45.4831			−1.45962			−0.729811	+	0.683649i	$0.760392\pi$
$972$		0			0
$973$	−65.1951			−2.09006
$974$		0			0
$975$	−0.544142	−	0.704213i	−0.0174265	−	0.0225529i
$976$		0			0
$977$	−1.01756	−	1.76246i	−0.0325545	−	0.0563861i	0.849289	−	0.527928i	$-0.177031\pi$
$977$	−1.01756	−	1.76246i	−0.0325545	−	0.0563861i	−0.881844	+	0.471542i	$0.843698\pi$
$978$		0			0
$979$	−40.2001	+	69.6286i	−1.28480	+	2.22534i
$980$		0			0
$981$	−6.31675	+	24.2265i	−0.201678	+	0.773493i
$982$		0			0
$983$	−12.7065	+	22.0083i	−0.405275	+	0.701957i	−0.994353	−	0.106119i	$-0.966157\pi$
$983$	−12.7065	+	22.0083i	−0.405275	+	0.701957i	0.589079	+	0.808076i	$0.299491\pi$
$984$		0			0
$985$	−6.84038	−	11.8479i	−0.217952	−	0.377505i
$986$		0			0
$987$	−19.2192	+	46.8451i	−0.611753	+	1.49110i
$988$		0			0
$989$	−6.02848			−0.191694
$990$		0			0
$991$	−0.259533			−0.00824435			−0.00412218	−	0.999992i	$-0.501312\pi$
$991$	−0.259533			−0.00824435			−0.00412218	+	0.999992i	$0.501312\pi$
$992$		0			0
$993$	−22.1390	+	2.99060i	−0.702559	+	0.0949037i
$994$		0			0
$995$	2.97706	+	5.15643i	0.0943793	+	0.163470i
$996$		0			0
$997$	24.4570	−	42.3608i	0.774561	−	1.34158i	−0.160479	−	0.987039i	$-0.551304\pi$
$997$	24.4570	−	42.3608i	0.774561	−	1.34158i	0.935041	−	0.354540i	$-0.115363\pi$
$998$		0			0
$999$	31.4932	−	13.4196i	0.996399	−	0.424576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.q.e.241.3	yes	8
3.2	odd	2		1080.2.q.e.721.1		8
4.3	odd	2		720.2.q.l.241.2		8
9.2	odd	6		3240.2.a.s.1.4		4
9.4	even	3	inner	360.2.q.e.121.3	✓	8
9.5	odd	6		1080.2.q.e.361.1		8
9.7	even	3		3240.2.a.u.1.4		4
12.11	even	2		2160.2.q.l.721.4		8
36.7	odd	6		6480.2.a.cb.1.1		4
36.11	even	6		6480.2.a.bz.1.1		4
36.23	even	6		2160.2.q.l.1441.4		8
36.31	odd	6		720.2.q.l.481.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.e.121.3	✓	8	9.4	even	3	inner
360.2.q.e.241.3	yes	8	1.1	even	1	trivial
720.2.q.l.241.2		8	4.3	odd	2
720.2.q.l.481.2		8	36.31	odd	6
1080.2.q.e.361.1		8	9.5	odd	6
1080.2.q.e.721.1		8	3.2	odd	2
2160.2.q.l.721.4		8	12.11	even	2
2160.2.q.l.1441.4		8	36.23	even	6
3240.2.a.s.1.4		4	9.2	odd	6
3240.2.a.u.1.4		4	9.7	even	3
6480.2.a.bz.1.1		4	36.11	even	6
6480.2.a.cb.1.1		4	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05903 + 1.37057i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.51859 + 2.63027i) q^{7} +(-0.756906 + 2.90295i) q^{9} +O(q^{10})\)	\(q+(1.05903 + 1.37057i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.51859 + 2.63027i) q^{7} +(-0.756906 + 2.90295i) q^{9} +(-2.63557 + 4.56494i) q^{11} +(0.256906 + 0.444974i) q^{13} +(0.657430 - 1.60243i) q^{15} +2.80320 q^{17} +8.29877 q^{19} +(-5.21319 + 0.704213i) q^{21} +(-2.51859 - 4.36232i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.78027 + 2.03692i) q^{27} +(2.39248 - 4.14389i) q^{29} +(4.29408 + 7.43756i) q^{31} +(-9.04771 + 1.22219i) q^{33} +3.03717 q^{35} -6.58816 q^{37} +(-0.337795 + 0.823348i) q^{39} +(-3.99088 - 6.91240i) q^{41} +(0.598399 - 1.03646i) q^{43} +(2.89248 - 0.795973i) q^{45} +(4.81267 - 8.33578i) q^{47} +(-1.11221 - 1.92640i) q^{49} +(2.96868 + 3.84198i) q^{51} -0.467941 q^{53} +5.27114 q^{55} +(8.78865 + 11.3740i) q^{57} +(0.378666 + 0.655869i) q^{59} +(0.135572 - 0.234817i) q^{61} +(-6.48610 - 6.39924i) q^{63} +(0.256906 - 0.444974i) q^{65} +(3.63080 + 6.28872i) q^{67} +(3.31159 - 8.07172i) q^{69} +1.48619 q^{71} +5.31701 q^{73} +(-1.71646 + 0.231865i) q^{75} +(-8.00469 - 13.8645i) q^{77} +(7.98175 - 13.8248i) q^{79} +(-7.85419 - 4.39451i) q^{81} +(-6.03240 + 10.4484i) q^{83} +(-1.40160 - 2.42764i) q^{85} +(8.21319 - 1.10946i) q^{87} +15.2529 q^{89} -1.56053 q^{91} +(-5.64611 + 13.7619i) q^{93} +(-4.14938 - 7.18694i) q^{95} +(3.18187 - 5.51116i) q^{97} +(-11.2569 - 11.1062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + q^7	\( 8 q - 4 q^{5} + q^{7} - q^{11} - 4 q^{13} + 3 q^{15} + 10 q^{17} + 2 q^{19} - 7 q^{23} - 4 q^{25} - 18 q^{27} - 7 q^{29} + 2 q^{31} - 3 q^{33} - 2 q^{35} + 12 q^{37} - 6 q^{39} - 12 q^{41} + 11 q^{43} - 3 q^{45} - 7 q^{47} - 3 q^{49} + 39 q^{51} + 24 q^{53} + 2 q^{55} + 27 q^{57} - 11 q^{59} - 19 q^{61} - 33 q^{63} - 4 q^{65} + 10 q^{67} - 9 q^{69} + 24 q^{71} + 18 q^{73} - 3 q^{75} - 32 q^{77} + 24 q^{79} - 12 q^{81} - 23 q^{83} - 5 q^{85} + 24 q^{87} + 42 q^{89} + 28 q^{91} + 18 q^{93} - q^{95} - q^{97} - 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 + q^7 - q^11 - 4 * q^13 + 3 * q^15 + 10 * q^17 + 2 * q^19 - 7 * q^23 - 4 * q^25 - 18 * q^27 - 7 * q^29 + 2 * q^31 - 3 * q^33 - 2 * q^35 + 12 * q^37 - 6 * q^39 - 12 * q^41 + 11 * q^43 - 3 * q^45 - 7 * q^47 - 3 * q^49 + 39 * q^51 + 24 * q^53 + 2 * q^55 + 27 * q^57 - 11 * q^59 - 19 * q^61 - 33 * q^63 - 4 * q^65 + 10 * q^67 - 9 * q^69 + 24 * q^71 + 18 * q^73 - 3 * q^75 - 32 * q^77 + 24 * q^79 - 12 * q^81 - 23 * q^83 - 5 * q^85 + 24 * q^87 + 42 * q^89 + 28 * q^91 + 18 * q^93 - q^95 - q^97 - 84 * q^99

Introduction

L-functions

Modular forms

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